Patches of particles (hair) on a plane following noise
The method I would use to clump the vegetation together is by tweaking the 'radius' value in the particle's children tab. Note that children type must be set to 'Simple'.




This is the most simple and easy way to achieve the 'bush' look, but if you want more freedom and customization possibilities, a density texture is the way to go!

For example: I'm using a cloud texture to control where the hair can grow and where not.

 


For this example I'm using a cloud texture, but you can obviously paint a texture by hand and gain 100% control.

Make sure to check the influence of your texture:


And assign it in the particle system as well:


A fundamental difference between these methods is that by using a texture, you're actually 'cutting' out portion of your scattered hair. By using the radius option under the children's panel, you control where the hair-particles are going to be scattered. So your amount of particles in the settings will be higher when using a texture.